Interplay between wall slip and shear banding in a thixotropic yield stress fluid.

We study the local dynamics of a thixotropic yield stress fluid that shows a pronounced non-monotonic flow curve. This mechanically unstable behavior is generally not observable from standard rheometry tests, resulting in a stress plateau that stems from the coexistence of a flowing band with an unyielded region below a critical shear rate c. Combining ultrasound velocimetry with standard rheometry, we discover an original shear-banding scenario in the decreasing branch of the flow curve of model paraffin gels, in which the velocity profile of the flowing band is set by the applied shear rate  instead of c. As a consequence, the material slips at the walls with a velocity that shows a non-trivial dependence on the applied shear rate. To capture our observations, we propose a differential version of the so-called lever rule, describing the extent of the flowing band and the evolution of wall slip with shear rate. This phenomenological model holds down to very low shear rates, at which the dimension of the flowing band becomes comparable to the size of the individual wax particles that constitute the gel microstructure, leading to cooperative effects. Our approach provides a framework where constraints imposed in the classical shear-banding scenario can be relaxed, with wall slip acting as an additional degree of freedom.

Tuning local microstructure of colloidal gels by ultrasound-activated deformable inclusions.

Colloidal gels possess a memory of previous shear events, both steady and oscillatory. This memory, embedded in the microstructure, affects the mechanical response of the gel, and therefore enables precise tuning of the material properties under careful preparation. Here we demonstrate how the dynamics of a deformable inclusion, namely a bubble, can be used to locally tune the microstructure of a colloidal gel. We examine two different phenomena of bubble dynamics that apply a local strain to the surrounding material: dissolution due to gas diffusion, with a characteristic strain rate of ∼10-3 s-1; and volumetric oscillations driven by ultrasound, with a characteristic frequency of ∼104 s-1. We characterise experimentally the microstructure of a model colloidal gel around bubbles in a Hele-Shaw geometry using confocal microscopy and particle tracking. In bubble dissolution experiments, we observe the formation of a pocket of solvent next to the bubble surface, but marginal changes to the microstructure. In experiments with ultrasound-induced bubble oscillations, we observe a striking rearrangement of the gel particles into a microstructure with increased local ordering. High-speed bright-field microscopy reveals the occurrence of both high-frequency bubble oscillations and steady microstreaming flow; both are expected to contribute to the emergence of the local order in the microstructure. These observations open the way to local tuning of colloidal gels based on deformable inclusions controlled by external pressure fields.

Acoustic bubble dynamics in a yield-stress fluid.

Yield-stress fluids naturally trap small bubbles when their buoyancy applies an insufficient stress to induce local yielding of the material. Under acoustic excitation, trapped bubbles can be driven into volumetric oscillations and apply an additional local strain and stress that can trigger yielding and assist their release. In this paper we explore different regimes of microbubble oscillation and translation driven by an ultrasound field in a model yield-stress fluid, a Carbopol microgel. We first analyse the linear bubble oscillation dynamics to measure the local, high-frequency viscosity of the material. We then use acoustic pressure gradients to induce bubble translation and examine the elastic part of the response of the material below yielding. We find that, at moderate pressure amplitude, the additional stresses applied by volumetric oscillations and acoustic radiation forces do not lead to any detectable irreversible bubble motion. At high pressure amplitude, we observe non-spherical shape oscillations that result in erratic bubble motion. The critical pressures we observe differ from the predictions of a recent model of shape oscillations in soft solids. Based on our findings, we discuss possible reasons for the lack of bubble release in Carbopol and suggest other systems in which ultrasound-assisted bubble rise may be observed.

Boundary-induced inhomogeneity of particle layers in the solidification of suspensions.

When a suspension freezes, a compacted particle layer builds up at the solidification front with noticeable implications on the freezing process. In a directional solidification experiment of monodisperse suspensions in thin samples, we evidence a link between the thickness of this layer and the sample depth. We attribute it to an inhomogeneity of particle density that is attested by the evidence of crystallization at the plates and of random close packing far from them. A mechanical model based on the resulting modifications of permeability enables us to relate the layer thickness to this inhomogeneity and to select the distribution of particle density that yields the best fit to our data. This distribution involves an influence length of sample plates of about 11 particle diameters. Altogether, these results clarify the implications of boundaries on suspension freezing. They may be useful to model polydisperse suspensions with large particles playing the role of smooth boundaries with respect to small ones.

Irreversible hardening of a colloidal gel under shear: The smart response of natural rubber latex gels.

Natural rubber is obtained by processing natural rubber latex, a liquid colloidal suspension that rapidly gels after exudation from the tree. We prepared such gels by acidification, in a large range of particle volume fractions, and investigated their rheological properties. We show that natural rubber latex gels exhibit a unique behavior of irreversible strain hardening: when subjected to a large enough strain, the elastic modulus increases irreversibly. Hardening proceeds over a large range of deformations in such a way that the material maintains an elastic modulus close to, or slightly higher than the imposed shear stress. Local displacements inside the gel are investigated by ultrasound imaging coupled to oscillatory rheometry, together with a Fourier decomposition of the oscillatory response of the material during hardening. Our observations suggest that hardening is associated with irreversible local rearrangements of the fractal structure, which occur homogeneously throughout the sample.

Wall friction and Janssen effect in the solidification of suspensions.

We address the mechanical effect of rigid boundaries on freezing suspensions. For this we perform the directional solidification of monodispersed suspensions in thin samples and we document the thickness h of the dense particle layer that builds up at the solidification front. We evidence a change of regime in the evolution of h with the solidification velocity V with, at large velocity, an inverse proportionality and, at low velocity, a much weaker trend. By modelling the force balance in the critical state for particle trapping and the dissipation phenomena in the whole layer, we link the former evolution to viscous dissipation and the latter evolution to solid friction at the rigid sample plates. Solid friction is shown to induce an analog of the Janssen effect on the whole layer. We determine its dependence on the friction coefficient between particles and plates, on the Janssen's redirection coefficient in the particle layer, and on the sample depth. Fits of the resulting relationship to data confirm its relevance at all sample depths and provide quantitative determinations of the main parameters, especially the Janssen's characteristic length and the transition thickness h between the above regimes. Altogether, this study thus clarifies the mechanical implication of boundaries on freezing suspensions and, on a general viewpoint, provides a bridge between the issues of freezing suspensions and of granular materials.

Interaction of Multiple Particles with a Solidification Front: From Compacted Particle Layer to Particle Trapping.

The interaction of solidification fronts with objects such as particles, droplets, cells, or bubbles is a phenomenon with many natural and technological occurrences. For an object facing the front, it may yield various fates, from trapping to rejection, with large implications regarding the solidification pattern. However, whereas most situations involve multiple particles interacting with each other and the front, attention has focused almost exclusively on the interaction of a single, isolated object with the front. Here we address experimentally the interaction of multiple particles with a solidification front by performing solidification experiments of a monodisperse particle suspension in a Hele-Shaw cell with precise control of growth conditions and real-time visualization. We evidence the growth of a particle layer ahead of the front at a close-packing volume fraction, and we document its steady-state value at various solidification velocities. We then extend single-particle models to the situation of multiple particles by taking into account the additional force induced on an entering particle by viscous friction in the compacted particle layer. By a force balance model this provides an indirect measure of the repelling mean thermomolecular pressure over a particle entering the front. The presence of multiple particles is found to increase it following a reduction of the thickness of the thin liquid film that separates particles and front. We anticipate the findings reported here to provide a relevant basis to understand many complex solidification situations in geophysics, engineering, biology, or food engineering, where multiple objects interact with the front and control the resulting solidification patterns.

Predicting and assessing rupture in protein gels under oscillatory shear.

Soft materials may break irreversibly upon applying sufficiently large shear oscillations, a process whose physical mechanism remains largely elusive. In this work, the rupture of protein gels made of sodium caseinate under an oscillatory stress is shown to occur in an abrupt, brittle-like manner. Upon increasing the stress amplitude, the build-up of harmonic modes in the strain response can be rescaled for all gel concentrations. This rescaling yields an empirical criterion to predict the rupture point way before the samples are significantly damaged. "Fatigue" experiments under stress oscillations of constant amplitude can be mapped onto the former results, which indicates that rupture is independent of the temporal pathway in which strain and damage accumulate. Finally, using ultrasonic imaging, we measure the local mechanical properties of the gels before, during and after breakdown, showing that the strain field remains perfectly homogeneous up to rupture but suddenly gives way to a solid-fluid phase separation upon breakdown.